I'm really trying to get my head around this one and our text doesn't give a very good example of this.(adsbygoogle = window.adsbygoogle || []).push({});

Problem:

A nonrelativistic particle of charge q and mass m is in a uniform magnetic field B in the z drection. The inital position is x=0, y=0, z=0; the magnitude of inital velocity of the particle is V_{0}.

What must be the direction of the initial velocity of the particle if it is to reach the point

x= a,2mv_{0}/qB, y=0, z=0 in the least possible time?

Assumtions:

1. If the transverse deflections are small, we can regard this velocity as constant and can say that the particle spends time t=l/v_{z}in the field.

2. The magnetic field gives the particle an acceleration in both the Y and Z direction which results in deflction in the Y direction?

The equation given in the text is tan(theta)_{y}= a_{y}t/v_{x}= eEl/mv^{2}_{x}

but it honestly doesn't state what this is or how it is derived.

I know this is alot of questioning, but any little bit helps. I'm still really trying to figure out what exactly is happening in the problem and how they came to use the equation.

Thanks.

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# Homework Help: Find direction of initial velocity of nonrelativistic particle in B

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